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Formal power series

  1. Feb 16, 2010 #1
    1. The problem statement, all variables and given/known data

    Let F be a field. Consider the ring R=F[[t]] of the formal power series
    in t. It is clear that R is a commutative ring with unity.

    the things in R are things of the form infiniteSUM{ a_n } = a_0 + a_1 t + a_2 t +...

    b is a unit iff the constant term a_0 =/= 0

    Prove that R is a Euclidean domain with respect to the norm N(b)=n if a_n is the first term of b that is =/= 0.

    In the polynomial ring R[x], prove that x^n-t is irreducible.



    3. The attempt at a solution
    I showed that it is a ED.

    How do I show Irreducibility of this thing?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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